Particle separation and concentration using spiral inertial filtration

ABSTRACT

A spiral inertial filtration device is capable of high-throughput (1 mL/min), high-purity particle separation while concentrating recovered target particles by more than an order of magnitude. Large fractions of sample fluid are removed from a microchannel without disruption of concentrated particle streams by taking advantage of particle focusing in inertial spiral microfluidics, which is achieved by balancing inertial lift forces and Dean drag forces. To enable the calculation of channel geometries in the device for specific concentration factors, an equivalent circuit model was developed and experimentally validated. Large particle concentration factors were achieved by maintaining either average fluid velocity or Dean number throughout the entire length of the channel during the incremental removal of sample fluid. Also provided is the ability to simultaneously separate more than one particle from the same sample.

PRIORITY CLAIM

This application is a divisional of U.S. patent application Ser. No.14/042,043, filed Sep. 30, 2013, which claims the benefit under 35U.S.C. § 119(e) of U.S. Provisional Application No. 61/707,878, filedSep. 28, 2012, each of which is incorporated herein by reference intheir entireties.

FIELD OF THE INVENTION

The present invention relates to the field of microfluidics, andspecifically relates to the field of sample preparation inmicrofluidics, including concentrating components of interest fromsamples. The present invention relates to methods of separating targetcomponents from biological samples such as blood sputum, etc. Accordingto the present invention, the components of interests may be white bloodcells, viruses, bacteria, fungi or combinations thereof. In someembodiments the components of interest may be cells having nuclei. Insome embodiments the cells are mammalian cells. In some embodiments, theseparated target organisms are subjected to treatment to release DNAwhich can then be recovered.

BACKGROUND OF THE INVENTION

High throughput particle separation and concentration are critical formany applications in the chemical, environmental, and biomedical fields.In particular, a number of cellular and sub-cellular purification andenrichment applications are used to enable the quantitative study anddiagnosis of disease. The diagnosis of infectious diseases relies on thedetection of relatively small amounts of infectious organisms (e.g.,viruses, bacteria, or fungi) in the blood stream or in other biologicalsamples. It may also be desirable to isolate other components fromsamples, including different types of cells (e.g., cancer cells, whiteblood cells, etc.). Once infectious organisms or components of interestare isolated from samples, they may then be used in further applicationsrelated to identification, including the isolation of nucleic acids fromthose components to allow downstream processing. Thus, a need exists formethods that provide for the enrichment and purification of componentsof interest from biological samples, including viruses, bacteria, fungi,cancer cells, and white blood cells.

Commercial products are available for cell separation, whole bloodfractionation, and subcellular fractionation using density gradients.However, these techniques have poor separation resolution and areinappropriate for recovering rare cells. Commercially availablefluorescence-activated cell sorting (FACS) systems enable automated cellseparation and counting, but cannot process large sample volumes and arealso inappropriate for recovering rare cells.

Many microfluidic techniques have emerged for sorting, concentrating, orpurifying particles and cells.¹⁻²⁰ Recent research into microfluidicdevices has enabled applications that include microorganism recoveryfrom environmental and biological samples²¹, white blood cell countingfor immune deficiency diagnosis²², and circulating tumor cell (CTC)counting for cancer metastasis diagnosis and prognosis^(23,24). Most ofthese techniques operate in the range of 1-100 μL/min, but asignificantly higher throughput is needed for applications that requireprocessing large volumes of fluid to obtain usable quantities of atarget species, such as rare cell concentration. Methods designed forrare cell recovery must therefore be capable of significantly reducingthe total fluid volume, from mL to 100 μL or less, to enable downstreammicrofluidic steps while preserving the rare targeted particles.

Recently, the need for high-throughput separation has been addressed byinertial-migration-based particle separation strategies, which arecapable of achieving greater than 1 mL/min throughput.²⁵ Thesestrategies balance forces within the channel to locate particles of acertain size into a desired longitudinal position. In a straightchannel, two inertial lift forces (F_(L)), one due to the parabolic flowprofile and the other due to the interaction of the particles with thewall, balance to focus particles to discrete equilibrium positions alongthe channel periphery.^(26,27) This was first shown by Segre andSilberberg²⁸ at the centimeter-scale and later by others for microscaleapplications.^(29-32,21,33-37)

The use of curvilinear geometries such as arc,³⁸⁻⁴³ asymmetricserpentine,⁴⁴⁻⁴⁶ and spiral⁴⁷⁻⁵⁶ channels introduces a third force, theDean force, F_(D), due to the formation of secondary flows, known asDean vortices. The magnitude of these secondary flows is described bythe dimensionless Dean number (De)^(57,58)

$\begin{matrix}{{De} = {\frac{\rho\; U_{f}D_{h}}{\mu}\sqrt{\frac{D_{h}}{2R}}}} & (1)\end{matrix}$where ρ is the density of the fluid, U_(f) is the average fluidvelocity, μ is the fluid dynamic viscosity, R is the radius of curvatureof the curvilinear channel, and D_(h) is the hydraulic diameter. Thehydraulic diameter, D_(h), is determined from

$\begin{matrix}{D_{h} = \frac{2{wh}}{w + h}} & (2)\end{matrix}$where w and h are the channel width and height, respectively. The Deanvortices are counter-rotating and act to laterally displace particlesacross the channel by imposing a drag force. The Dean force acts incombination with the combined lift forces to alter the equilibriumpositions of focused particles to a single equilibrium position near theinner wall of the channel.

FIG. 1A is a schematic diagram of a microfluidic channel cross-sectionillustrating the principle of inertial spiral microfluidics. The mainflow (into the page) follows a curvilinear path leading to thedevelopment of secondary flows, known as Dean vortices (dashed lines).Dispersed particles experience a combination of lift forces (F_(L)) andDean forces (F_(D)), which result in differential migration of theparticles to unique equilibrium positions near the inner wall.

The lift forces go as F_(L)∝α_(p) ⁴ and the Dean forces go asF_(D)∝α_(p), where α_(p) is particle diameter. The equilibrium positionis thus particle-size-dependent, with larger particles (dominated byF_(L)) aligning near the inner wall and smaller particles (dominated byF_(D)) near the channel center⁴⁷. An example of a two-particleseparation in a microfluidic spiral is shown in FIG. 1B. Particles ofone size (e.g., 15 μm) are separated from particles of a different size(e.g., 8 μm) at a flow rate of 1 mL/min.

Spiral inertial microfluidic devices have been successfully used in awide range of applications including particle^(47,49,51,54) and cell⁴⁹separations, cell synchronization,⁵⁰ circulating tumor cell isolation,⁵⁹and electroporation.⁵⁵ These devices typically utilize a branched outletto collect the concentrated, focused particle or cell streams. Theseparation efficiency for a device is defined as the number of targetedparticles collected at a single outlet over the number of thoseparticles input into the device. The concentration factor is defined asthe concentration of particles, assuming 100% recovery, over the inletpartial concentration multiplied by the separation efficiency.Ultimately, for any geometry, the concentration factor is limited by thenumber of outlets: if there are too many, a particle stream cannot beprecisely controlled to flow through a single one. Devices with branchedoutlets of up to eight channels have been shown⁴⁹. This resulted in aconcentration factor of 8× (i.e., 87.5% removal of the inlet fluid).Using only branched outlets, however, further increases in concentrationfactor to greater than 10× (90% fluid removal) are challenging. Forexample, 93% removal corresponds to a 14× concentration factor, whichwould require 14 outlets. The width of the outlets typically needs to be4-5 times the particle diameter to ensure that the particle stream iscollected in a single outlet. A large number of outlets, therefore, thusrequires a large expansion of the width of the channel in front of theoutlets. This expansion is accompanied by a corresponding increase inthe width of the fluid streamlines, and thus the width of the particlestream, which becomes too wide to be collected in a single outletchannel, leading to particle loss and a decrease in separationefficiency.

Increasing particle concentration and purity in a microfluidic device byremoving, or “skimming”, fluid from a main channel through microfluidicwaste channels has been previously reported. Traditional skimmingtechniques rely on the natural formation of small particle-free regionsnear channel walls⁶⁰⁻⁶⁴ (as shown in FIG. 2A) or geometrical features⁶⁵(as shown at FIG. 2B). In one approach, posts^(66,67) or dams⁶⁸ locatedat the outer wall were used to filter particles. Fluid and smallerparticles were able to pass through the post or dam filters and wereremoved, while larger particles were retained. These devices wereoperated at low flow rates (<100 μL/min) in order to minimize theinertial effects and the secondary Dean flows. As a result, centrifugalforces dominated and pushed particles to the outside wall of thecurvilinear channels. Another design took advantage of centrifugalforces to push blood cells against the outer wall and remove plasma froma waste channel on the inner wall.³⁸ Flow rates up to 120 μL/min wereachieved. In a third approach, inertial lift forces focused targetedcells away from the walls, creating a target-free region where wastechannels removed fluid and non-targeted cells^(69,70); this designachieved>500 μL/min. These devices focused on enriching targeted cellsrelative to high-concentration, non-targeted species, and were notaiming to achieve high concentration factors.

SUMMARY OF THE INVENTION

The present invention relates to methods of separating particles withinsamples, for example, separating target DNA, from mixed DNA in a sample.In some, non-limiting embodiments, the target DNA is present in targetorganisms, such as viruses, bacteria (prokaryotes), fungi orcombinations thereof. In some embodiments the mixed DNA includes targetDNA and non-target DNA. In some embodiments, the non-target DNA ismammalian DNA. In some embodiments the sample contains cells havingnuclei. In some embodiments the cells are mammalian cells. In someembodiments, the separated target organisms are treated to release theirDNA which can be recovered.

In one embodiment of the present invention, there is provided a methodof designing a spiral inertial filtration device as provided herein.

In a second embodiment of the present invention, there is provided amethod of separating a component of interest from a sample comprisingintroducing the sample to a spiral inertial filtration device asprovided herein.

In a further embodiment, the spiral inertial filtration device comprisesat least one waste channel configured to draw particle-free fluid fromthe device, thereby increasing the particle concentration of fluid(sample) remaining in the device.

In another embodiment, the waste channels reduce the volume of thesample from about 10% to about 95%, ie. about 10%, about 15%, about 20%,about 25%, about 30%, about 35%, about 40%, about 45%, about 50%, about55%, about 60%, about 65%, about 70%, about 75%, about 80%, about 85%,about 90%, or about 95%.

In a further embodiment, the component of interest is concentrated bythe spiral inertial filtration device.

In another embodiment, the component of interest is selected fromviruses, bacteria, fungi, cancer cells, and white blood cells. In afurther embodiment, the component of interest is neutrophils.

One embodiment of the present invention provides a spiral inertialfiltration device as described herein.

Another embodiment of the present invention provides a spiral inertialfiltration device as described herein, wherein the device concentratesand/or filters more than one component of interest from the same sample.

A further embodiment of the present invention provides a method ofconcentrating and/or filtering more than one component of interest froma sample using a spiral inertial filtration device as provided herein.

In particular, aspects of the invention are embodied in a fluidprocessing apparatus configured for separating particles from a fluidflowing through the apparatus and comprising a fluid inlet, a main fluidchannel, one or more outlets, and one or more secondary channels. Thefluid inlet configured to receive a fluid containing particles havingone or more particle sizes. The a main fluid channel extends from thefluid inlet, is arranged in a spiral configuration, and is configured tocause differential migration of particles within the fluid flowingthrough the main fluid channel into unique equilibrium positions withinthe main channel according to the size of the particle, thereby formingone or more particle streams and a particle-free region within the fluidflowing through the main channel. The one or more outlets are in fluidcommunication with the main fluid channel and are configured to receiveparticles from a particle stream flowing from the main fluid channel.The one or more secondary channels extend from the main fluid channeland are configured to draw at least a portion of the fluid from theparticle-free region within the main channel to increase theconcentration of particles within the remaining fluid flowing throughthe main channel.

According to further aspects of the invention, the particles of each ofthe one or more particle streams is maintained in an equilibriumposition by lift forces F_(L) and Dean forces F_(D).

According to further aspects of the invention, the one or more particlessizes are in a range of 4.8 μm to 15 μm.

According to further aspects of the invention, the secondary channelsare configured to draw a portion of the fluid of the particle-freeregion from the main channel to reduce the volume of fluid flowingthrough the main channel by about 10-95%.

According to further aspects of the invention, the particles areselected from the group consisting of DNA molecules, viruses, bacteria,fungi, cancer cells, white blood cells, and neutrophils.

According to further aspects of the invention, the fluid flowing throughthe apparatus comprises a sample and the particles comprise more thanone component of interest within the sample, and the fluid inlet isconfigured to receive the sample, the main fluid channel is configuredso that the components of interest are focused into more than onecomponent stream according to the size of the components, therebyforming a component-free region within the fluid flowing through themain channel, the apparatus includes more than one outlet in fluidcommunication with the main fluid channel and configured to receive thecomponents of interest from the component streams flowing from the mainfluid channel to filter each of the components of interest from thesample, and the one or more secondary channels are configured to draw atleast a portion of the fluid from the component-free region within themain channel to increase the concentration of components of interestwithin the remaining fluid flowing through the main channel.

According to further aspects of the invention, the fluid inlet islocated at an inner end portion of the spiral configuration of the mainchannel, the one or more outlets are located at an outer end portion ofthe spiral configuration of the main channel, and the one or moresecondary channels extend radially outwardly from an outer loop of thespiral configuration of the main channel.

According to further aspects of the invention, the main channel has anon-uniform width varying along the length of the main channel.

According to further aspects of the invention, the apparatus includes atleast two secondary channels, and the width of the main channel issubstantially constant between each two neighboring secondary channels.

According to further aspects of the invention, the geometry of the mainchannel is changed following a secondary channel to compensate for fluidremoval via the secondary channel.

According to further aspects of the invention, the geometry of the mainchannel is changed following a secondary channel to maintain a constantor substantially constant flow velocity within the main channel beforeand after the secondary channel.

According to further aspects of the invention, the geometry of the mainchannel is changed by changing the width of the main channel, and thenew width w_(m,j) of the main channel following a j^(th) secondarychannel is determined by the formula:w_(m,j-1)=x_(m,j-1)w_(m,j),wherein x_(mj-1) is the fraction of fluid remaining in the main channelafter fluid removal through the j^(th) secondary channel, and w_(m,j) isthe width of the previous section of the main channel.

According to further aspects of the invention, the geometry of the mainchannel is changed following a secondary channel to maintain a constantor substantially constant Dean number, D_(e), within the main channelbefore and after the secondary channel, wherein the Dean number, D_(e),is given by the formula:

${De} = {\frac{{\rho U}_{f}D_{h}}{\mu}\sqrt{\frac{D_{h}}{2R}}}$wherein ρ is the density of the fluid, U_(f) is average fluid velocity,μ is fluid dynamic viscosity, R is the radius of curvature of the mainchannel, and D_(h) is a hydraulic diameter, and wherein the hydraulicdiameter, D_(h), is determined from:

${D_{h} = \frac{2{wh}}{w + h}},$wherein w is the width of the main channel and h is the height of themain channel.

According to further aspects of the invention, the geometry of the mainchannel is changed by changing the width of the main channel.

According to further aspects of the invention, a downstream corner of ajunction between the main channel and the secondary channel is filletedto allow for a gradual change in the width of the main channel.

According to further aspects of the invention, that apparatus comprisesbetween one and five outlets.

According to further aspects of the invention, that apparatus comprisesbetween one and six secondary channels.

According to further aspects of the invention, each secondary channelextends from an outer edge of an outer-most ring of the spiralconfiguration of the main channel.

According to further aspects of the invention, each of the one or moresecondary channels is configured to draw from 5 to 50% of the fluidflowing through the main channel.

According to further aspects of the invention, each secondary channelcomprises a meander path.

According to further aspects of the invention, the apparatus isfabricated from polydimethylsiloxane.

According to further aspects of the invention, the apparatus isconfigured to accommodate a flow rate of between 100 μL/min and 1250μL/min.

According to further aspects of the invention, the apparatus isconfigured to process fluid at a rate of 1 mL/min.

According to further aspects of the invention, the width of eachsecondary channel is set to draw a specified portion of the fluid of theparticle-free region from the main channel according to the formula:

${w \approx {\frac{12\mu\; L}{h^{3}R_{H}} + {0.63\mspace{11mu} h}}},$wherein w is the width of the secondary channel, h is the height of thesecondary channel, L is the length of the secondary channel, μ is thedynamic viscosity of the fluid, and R_(H) is the hydraulic resistance ofthe secondary channel.

According to further aspects of the invention the fluid resistance of asecondary channel required to draw fluid from the main channel at aspecified rate satisfies the relationship:

$R_{s,j} = {r_{Q,j}( {R_{m,j} + \frac{R_{s,{j - 1}}}{1 + r_{Q,{j - 1}}}} )}$where R_(s,j) is the fluid resistance of the j^(th) secondary channel atthe j^(th) node where the j^(th) secondary channel connects to the mainchannel, R_(m,j) is the fluid resistance of the main channel at thej^(th) node, R_(s,j-1) is the fluid resistance of the secondary channelat a previous node j-1, and r_(Qj-1) is the volumetric flow ratio offlow within the main channel (Q_(m,j)) to flow within the secondarychannel (Q_(s,j)) at the j^(th) node.

According to further aspects of the invention, the spiral configurationof the main channel comprises a 6 or 7-loop spiral.

According to further aspects of the invention, the main channelcomprises a width of about 250 μm and a height of about 50 μm.

According to further aspects of the invention, the apparatus comprises asingle inlet, a single secondary channel, and a bifurcating outlet, andthe spiral main channel has a 250 μm gap between successive loops.

According to further aspects of the invention, the spiral configurationis an Archimedean spiral.

According to further aspects of the invention, the width of thesecondary channel is between 40 and 250 μm

According to further aspects of the invention, the length of thesecondary channel is about 19 mm.

According to further aspects of the invention, each secondary channelcomprises a width of about 35 μm, a height of about 50 μm, and a lengthof about 19 mm.

Further aspects of the invention are embodied in a method of filteringand/or concentrating particles of a fluid containing particles of one ormore particle sizes. A fluid is moved in a spiral path under conditionsthat cause differential migration of particles within the moving fluidinto unique equilibrium positions according to the size of the particlethereby forming one or more particle streams and a particle-free regionwithin the moving fluid. At least a portion of the fluid is drawn fromthe particle-free region of the moving fluid to increase theconcentration of particles within the remainder of the moving fluid, andparticles from one or more of the particle streams are collected.

According to further aspects of the invention, the collecting step isperformed at the end of the spiral path.

According to further aspects of the invention, the particles compriseone or more components of interest within a sample fluid.

According to further aspects of the invention, the method furthercomprises increasing the concentration of each component of interest.

According to further aspects of the invention, the particles of each ofthe one or more particle streams are maintained in equilibrium positionsby lift forces F_(L) and Dean forces F_(D).

According to further aspects of the invention, the one or more particlessizes are in a range of 4.8 μm to 15 μm.

According to further aspects of the invention, the drawing step reducesthe volume of the moving fluid by about 10-95%.

According to further aspects of the invention, the particles areselected from the group consisting of DNA molecules, viruses, bacteria,fungi, cancer cells, white blood cells, and neutrophils.

According to further aspects of the invention, the method furthercomprises changing the conditions of the moving fluid after drawing atleast a portion of the fluid from the particle-free region of the movingfluid to compensate for fluid removal.

According to further aspects of the invention, the method furthercomprises changing the conditions of the moving fluid after drawing atleast a portion of the fluid from the particle-free region of the movingfluid to maintain a constant or substantially constant flow velocitywithin the moving fluid before and after drawing at least a portion ofthe fluid from the particle-free region of the moving fluid.

According to further aspects of the invention, the method furthercomprises changing the conditions of the moving fluid after drawing atleast a portion of the fluid from the particle-free region of the movingfluid to maintain a constant or substantially constant Dean numberbefore and after drawing at least a portion of the fluid from theparticle-free region of the moving fluid.

41. The method of claim 30, wherein the moving fluid comprises a flowrate of between 100 μL/min and 1250 μL/min.

According to further aspects of the invention, the method comprisesfiltering and/or concentrating fluid containing particles of one or moreparticle sizes at a rate of 1 mL/min.

According to further aspects of the invention, the step of moving fluidin a spiral path is performed in a main fluid channel extending from afluid inlet and arranged in a spiral configuration, the step of drawingat least a portion of the fluid from the particle-free region of themoving fluid is performed in one or more secondary channels extendingfrom the main fluid channel, and the step of collecting particles fromone or more of the particle streams is performed with one or moreoutlets in fluid communication with the main fluid channel.

According to further aspects of the invention, the main channel has anon-uniform width varying along the length of the main channel.

According to further aspects of the invention, the step of drawing atleast a portion of the fluid from the particle-free region of the movingfluid is performed by at least two secondary channels, and the width ofthe main channel is substantially constant between each two neighboringsecondary channels.

According to further aspects of the invention, the one or more secondarychannels extend radially outwardly from an outer loop of the spiralconfiguration of the main channel.

According to further aspects of the invention, the method furthercomprises changing the geometry of the main channel following asecondary channel to compensate for fluid removal via the secondarychannel.

According to further aspects of the invention, the method furthercomprisies changing the geometry of the main channel following thesecondary channel to maintain a constant or substantially constant flowvelocity within the main channel before and after the secondary channel.

According to further aspects of the invention, the method furthercomprises changing the geometry of the main channel by changing thewidth of the main channel, and the new width w_(m,j) of the main channelfollowing a j^(th) secondary channel is determined by the formula:w_(m,j-1)=x_(m,j-1)w_(m,j),wherein x_(m,j-1) is the fraction of fluid remaining in the main channelafter fluid removal through the j^(th) secondary channel, and w_(m,j) isthe width of the previous section of the main channel.

According to further aspects of the invention, the method furthercomprises changing the geometry of the main channel following asecondary channel to maintain a constant or substantially constant Deannumber, D_(e), within the main channel before and after the secondarychannel, the Dean number, D_(e), is given by the formula:

${De} = {\frac{\rho\; U_{f}D_{h}}{\mu}\sqrt{\frac{D_{h}}{2R}}}$and ρ is the density of the fluid, U_(f) is average fluid velocity, μ isfluid dynamic viscosity, R is the radius of curvature of the mainchannel, and D_(h) is a hydraulic diameter, and the hydraulic diameter,D_(h), is determined from:

${D_{h} = \frac{2{wh}}{w + h}},$and w is the width of the main channel and h is the height of the mainchannel.

According to further aspects of the invention, the fluid resistance of asecondary channel required to draw fluid from the main channel at aspecified rate satisfies the relationship:

$R_{s,j} = {r_{Q,j}( {R_{m,j} + \frac{R_{s,{j - 1}}}{1 + r_{Q,{j - 1}}}} )}$where R_(s,j) is the fluid resistance of the j^(th) secondary channel atthe j^(th) node where the j^(th) secondary channel connects to said mainchannel, R_(m,j) is the fluid resistance of said main channel at thej^(th) node, R_(s,j-1) is the fluid resistance of the secondary channelat a previous node j-1, and r_(Qj-1) is the volumetric flow ratio offlow within said main channel (Q_(m,j)) to flow within the secondarychannel (Q_(s,j)) at the j^(th) node.

According to further aspects of the invention, the method furthercomprises changing the geometry of the main channel by changing thewidth of the main channel.

According to further aspects of the invention, the method furthercomprises collecting particles from each particle stream with betweenone and five outlets.

According to further aspects of the invention, the method furthercomprises drawing at least a portion of the fluid from the particle-freeregion of the moving fluid with between one and six secondary channels.

According to further aspects of the invention, each secondary channelextends from an outer edge of an outer-most ring of the spiralconfiguration of the main channel.

According to further aspects of the invention, the method comprisesdrawing from 5 to 50% of the moving fluid in the main channel with eachof the one or more secondary channels.

According to further aspects of the invention, the method furthercomprises defining the width of each secondary channel to draw aspecified portion of the fluid of the particle-free region from the mainchannel according to the formula:

${w \approx {\frac{12\mu\; L}{h^{3}R_{H}} + {0.63\mspace{11mu} h}}},$wherein w is the width of the secondary channel, h is the height of thesecondary channel, L is the length of the secondary channel, μ is thedynamic viscosity of the fluid, and R_(H) is the hydraulic resistance ofthe secondary channel.

According to further aspects of the invention, the spiral configurationof the main channel comprises a 7-loop spiral having an inner radius ofabout 0.5 cm, and the main channel comprises a width of about 250 μm anda height of about 50 μm.

According to further aspects of the invention, the spiral main channelhas a 250 μm gap between successive loops.

According to further aspects of the invention, the width of eachsecondary channel is between 40 and 250 μm

According to further aspects of the invention, the length of eachsecondary channel is about 19 mm.

According to further aspects of the invention, each secondary channelcomprises a width of about 35 μm, a height of about 50 μm, and a lengthof about 19 mm.

Further aspects of the invention are embodied in a method of separatingone or more components of interest from a sample fluid, comprising thesteps of moving the sample fluid in a spiral path under conditions thatcause the component(s) of interest within the moving sample fluid to befocused into one or more component streams according to component size,thereby forming a component-free region within the moving sample fluid,drawing at least a portion of the sample fluid from the component-freeregion of the moving sample fluid to increase the concentration ofcomponent(s) of interest within the remainder of the moving samplefluid, and collecting the component(s) of interest from one or more ofthe component streams.

The above and other embodiments of the present invention are describedbelow with reference to the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated herein and form partof the specification, illustrate various embodiments of the presentinvention. In the drawings, like reference numbers or labels indicateidentical or functionally similar elements.

FIG. 1A is a schematic diagram of a microfluidic channel cross-section,illustrating the principle of inertial spiral microfluidics according toprior art.

FIG. 1B is a top view of a portion of a spiral microfluidic channelaccording to prior art illustrating differential migration of particlesinto unique equilibrium positions according to the size of the particlethereby forming discrete, focused particle streams and a particle-freeregion within the channel.

FIGS. 2A and 2B are prior art schematic diagrams illustrating thecreation of particle-free flow regions in straight channels (FIG. 2A)and expansions (FIG. 2B).

FIG. 3 is a schematic diagram illustrating the creation of particle-freeflow region in a curvilinear channel.

FIG. 4 is a schematic diagram of a spiral inertial filtration (SIFT)device embodying aspects of the invention.

FIG. 5A is a schematic diagram of a fluidic network including a mainchannel and a plurality of waste, or secondary, channels extending fromthe main channel.

FIG. 5B is a diagram of an equivalent circuit analog used to design anapparatus embodying aspects of the present invention.

FIG. 6A is a schematic diagram illustrating the dimensions of a devicewith a main channel and a single waste channel located at the W2position of the device shown in FIG. 4.

FIG. 6B is a graph showing dependency of actual fluid removed from awaste channel—as a percentage of fluid introduced at the inlet andflowing in the main channel—on the fluid flow rate for waste channelsdesigned for 5%, 10%, 20%, and 50% fluid removal.

FIG. 7 represents images of 15 μm particles focused in SIFT deviceshaving a single waste channel designed for 5% (i and ii), 20% (iii andiv), and 50% (v and vi) fluid removal at two flow rates (100 μL/min and1250 μL/min).

FIG. 8A represents particle focusing results for SIFT devices with themain channel widths corrected to maintain Dean number, De, followingfluid removal from the main channel via a waste channel.

FIG. 8B represents particle focusing results for SIFT devices with themain channel widths corrected to maintain average fluid velocity, U_(f),following fluid removal from the main channel via a waste channel.

FIG. 9A represents fluorescent images showing the separation of twoparticle sizes, 4.8 μm and 8 μm, in a SIFT device designed for removalof 93% of the inlet fluid.

FIG. 9B is a graph of separation efficiency, calculated as the number ofparticles collected at each outlet O1-O5 or waste channel W1-W6, overthe number input into the device.

FIG. 9C is a graph of particle concentration factor (concentration ateach outlet or waste channel, assuming 100% recovery, over the inletconcentration multiplied by the separation efficiency).

FIG. 10 is a diagram of an equivalent circuit for a device with threewaste channels having resistances R_(s) and a main channel with threesegments of resistance R_(m).

FIG. 11 is a diagram of an equivalent resistance R_(EQ,2) that replacesR_(m,2), R_(m,1), and R_(s,1).

FIG. 12 represents fluorescent images showing the separation intoparticle streams of two particle sizes, 4.8 μm (bottom) and 8 μm (top),in a SIFT device designed for removal of 93% of the inlet fluid.

DETAILED DESCRIPTION OF THE EXEMPLARY EMBODIMENTS

The present invention has several embodiments and relies on patents,patent applications and other references for details known to those ofthe art. Therefore, when a patent, patent application, or otherreference is cited or repeated herein, it should be understood that itis incorporated by reference in its entirety for all purposes as well asfor the proposition that is recited.

Unless defined otherwise, all terms of art, notations and othertechnical terms or terminology used herein have the same meaning as iscommonly understood by one of ordinary skill in the art to which thisdisclosure belongs. If a definition set forth in this section iscontrary to or otherwise inconsistent with a definition set forth in thepatents, applications, published applications, and other publicationsthat are herein incorporated by reference, the definition set forth inthis section prevails over the definition that is incorporated herein byreference.

The use of the terms “a” and “an” and “the” and similar referents in thecontext of describing the invention (especially in the context of thefollowing claims) are to be construed to cover both the singular and theplural, unless otherwise indicated herein or clearly contradicted bycontext. The terms “comprising,” “having,” “including,” and “containing”are to be construed as open-ended terms (i.e., meaning “including, butnot limited to,”) unless otherwise noted. Recitation of ranges of valuesherein are merely intended to serve as a shorthand method of referringindividually to each separate value falling within the range, unlessotherwise indicated herein, and each separate value is incorporated intothe specification as if it were individually recited herein. Forexample, if the range 10-15 is disclosed, then 11, 12, 13, and 14 arealso disclosed. All methods described herein can be performed in anysuitable order unless otherwise indicated herein or otherwise clearlycontradicted by context. The use of any and all examples, or exemplarylanguage (e.g., “such as”) provided herein, is intended merely to betterilluminate the invention and does not pose a limitation on the scope ofthe invention unless otherwise claimed. No language in the specificationshould be construed as indicating any non-claimed element as essentialto the practice of the invention.

This description may use relative spatial and/or orientation terms indescribing the position and/or orientation of a component, apparatus,location, feature, or a portion thereof. Unless specifically stated, orotherwise dictated by the context of the description, such terms,including, without limitation, top, bottom, above, below, under, on topof, upper, lower, left of, right of, in front of, behind, next to,adjacent, between, horizontal, vertical, diagonal, longitudinal,transverse, etc., are used for convenience in referring to suchcomponent, apparatus, location, feature, or a portion thereof in thedrawings and are not intended to be limiting.

Furthermore, unless otherwise stated, and specific dimensions mentionedin this description are merely representative of an exemplaryimplantation of a device embodying aspects of the invention and are notintended to be limiting.

The present invention relates to methods of separating particles, suchas target DNA, from mixed DNA in a sample. In some embodiments, thetarget DNA is present in target organisms. In some embodiments, thetarget organisms may be viruses, bacteria (prokaryotes), fungi orcombinations thereof. In some embodiments the mixed DNA includes targetDNA and non-target DNA. In some embodiments, the non-target DNA ismammalian DNA. In some embodiments the sample contains cells havingnuclei. In some embodiments the cells are mammalian cells. In someembodiments, the separated target organisms are treated to release theirDNA which can be recovered.

Thus, the present invention provides a method of increasing theconcentration factor of spiral inertial microfluidics while relaxing therequirements for the number of branched outlets, through a new approachknown as Spiral Inertial FilTration (SIFT). This technique utilizes thefocusing behavior of inertial microfluidics in a main microfluidicchannel having a spiral geometry to create a large particle-free flowregion from which a large fraction of particle-free (or substantiallyparticle free) fluid can be “skimmed” through one or more wastechannels, or secondary channels, extending from one or more portions ofthe main channel. The major drawback of skimming techniques describedabove is that the performance drops at increased flow rates. In SIFT,particles are instead focused near the inner wall, creating a largeparticle-free region at the outer wall (as shown in FIG. 3). Inaccordance with aspects of the invention, by utilizing side wastechannels that extend away from the outer wall of the main, spiralchannel, fluid can be removed from this particle-free region, thusincreasing the concentration of the particles in the main microfluidicchannel. In addition, due to the focusing nature of spiral inertialmicrofluidics, the particle streams are minimally disrupted by removinglarge amounts of fluid.

Leveraging this concept, the SIFT system utilizes waste channelsextending from the outer edge of the outer-most ring of the spiral togenerate a large concentration factor. FIG. 4 is a schematic diagram ofa spiral inertial filtration (SIFT) device embodying aspects of theinvention. The device includes an inlet (406) at which a fluidcontaining particles of one or more sizes is introduced into the device(400), a microfluidic, main channel (402) coiled in a spiralconfiguration, and one or more outlets (408). In the illustratedembodiment, the device includes five outlets O1-O5. In practice,however, the device (400) may have fewer than or more than five outlets(408). In the illustrated embodiment, the inlet (406) is located at aninner part of the spiral configuration of the main channel (402), andthe outlets O1-O5 are located at an outer end portion of the spiralconfiguration. As the fluid flows through the main channel from theinlet (406) toward the outlets, the particles within the fluid segregateinto separate, focused streams, according to the size of the particle,as explained above, thereby creating substantially particle-free regionswithin the fluid flowing through the main channel. Fluid (particle-freeor substantially particle-free) is removed from the main spiral channelthrough one or more waste, or secondary, channels (404) labeled W1-W6starting closest to the outlet(s). The illustrated embodiment includesix secondary channels W1-W6. In practice, the device may have fewerthan or more than six secondary channels (404). In the illustratedembodiment, the waste channels (404) extend radially outwardly from theoutermost loop of the spiral configuration. Concentrated particlestreams, each comprising particles of a different size, are collectedthrough one of outlets O1-O5. The device (400) may be fabricated from amaterial such as polydimethylsiloxane (PDMS) prepolymer, examples ofwhich are described in further detail below. Other suitable materialsinclude thermal plastics (e.g., Poly(methyl methacrylate) (“PMMA”), orCyclic Olefin Copolymer (“COC”)) and glass/silicon.

In other implementations, the particle, or component, of interest doesnot readily migrate to a unique equilibrium position under the effectsof lift forces (F_(L)) and/or Dean forces (F_(D)), and thus does notfocus into a discrete particle stream as shown in FIG. 1B. For example,viruses and bacteria can, in some circumstance, be difficult to separatefrom a flow stream using the inertial filtration techniques describedherein. Such non-focused components can be collected through thesecondary channels and can be focused by other means and removed fromthe waste fluid.

It was demonstrated that the SIFT design concept presented in FIG. 4 iscapable of recovering a targeted particle size with nearly perfectseparation efficiency and concentrating the targeted particles by morethan an order of magnitude while operating at a sample processing rateof 1 mL/min. Aspects of the invention include the development ofequations for designing a SIFT device for specific fluid removal.Validation of the design equations was demonstrated by removal of adesired fraction of the sample fluid (without removing targetedparticles) by controlling the channel geometries. The experimentalresults demonstrated that the amount of fluid removed from the sample islimited by changes in particle position and particle stream width causedby decreases in the linear velocity in the channel, U_(f), and the Deannumber, De, as fluid is removed.

Aspects of the invention further include the determination that thelimitations on larger fluid removal rates can be overcome by correctingthe main channel geometry to maintain U_(f) or De following fluidremoval through a waste channel. Finally, separation and recovery of twoparticle sizes (4.8 μm and 8 μm) was demonstrated using a SIFT devicewith 6 waste channels (404) and 5 outlets (408) (as in the device ofFIG. 4). The particle sizes selected were for demonstration purposes andare not limiting as to the scope of the invention as the invention maybe implemented to filter and/or concentrate particles of other sizes aswe. Using this design, nearly 100% separation efficiency of the twoparticle sizes was demonstrated while removing 93% of the inlet fluid,which leads to a 13× concentration increase of each of the recoveredparticle sizes.

Spiral Inertial Filtration Design Principle

For the derivation of equations for designing waste channels configuredfor the removal of specific volumes of fluid from the SIFT devices, anequivalent circuit analog^(60,71) was used. The volumetric flow rate (Q)was determined usingΔP=QR_(H)   (3)where ΔP is the pressure drop and R_(H) is the fluidic resistance. Theflow removed by any given waste channel is specified by the ratio offluidic resistances of the waste channel and the main channel. FIG. 5Ais a schematic diagram of a fluidic network including a main channel(502) and a plurality of waste, or secondary, W₁-W_(n) channels (504). Aschematic of the equivalent electrical circuit is shown in FIG. 5B. Thesubscripts “m” and “s” represent the main channel and secondarychannels, respectively. The flow rate at the inlet of the device isanalogous to a current source, and all outlets are terminated at ground,as they have the same pressure. For a volumetric flow ratio, r_(Q,j), ofthe main channel (Q_(m,j)) to a side waste channel at the j^(th) node(Q_(s,j)), the resistance relationship between the main and wastechannels satisfies

$\begin{matrix}{R_{s,j} = {r_{Q,j}( {R_{m,j} + \frac{R_{s,{j - 1}}}{1 + r_{Q,{j - 1}}}} )}} & (4)\end{matrix}$where R_(s,j)and R_(m,j) are the resistances of the waste channel andmain channel at the j^(th) node, respectively, R_(s,j-1) is theresistance of the waste channel at the previous node j-1, and r_(Q,j-1)is the volumetric flow ratio at the previous node (see below for aderivation of Equation (4))—this holds for j=2, 3, 4, . . . , n−1, n.For j=1, the resistance is simply R_(s,1)=r_(Q,1)R_(m,1). The entirecircuit does not need to be solved simultaneously. Equation (4)illustrates that once r_(Q,j) is specified, the resistance of the wastechannel, R_(s,j), at any node is determined only by the resistance inthe main channel, R_(m,j), the resistance of the previous waste channel,R_(s,j-1), and the flow ratio of the previous waste channel, r_(Q,j-1).Using this relationship, the resistance required to achieve a specifiedfluid removal can be determined, and from that relationship, thegeometry, e.g., the width, of the secondary waste channel can bedetermined.

Once the resistances of the main channel and the waste channels arecalculated, the channel dimensions can be calculated. For w>h or w≈h,the hydraulic resistance of a square duct is given by⁷²

$\begin{matrix}{R_{H} = {\frac{12\mu\; L}{{wh}^{3}}( {1 - {\frac{192\mspace{14mu} h}{\pi^{5}w}{\sum\limits_{{n = 1},3,5,\;\ldots}^{\propto}\frac{\tanh( \frac{n\;\pi\; w}{2\mspace{14mu} h} )}{n^{5}}}}} )^{- 1}}} & (5)\end{matrix}$where μ is the fluid dynamic viscosity and w, h, and L are the width,height, and length of the channel. If w>h, Equation (5) simplifies to⁷²

$\begin{matrix}{R_{H} \approx {\frac{12\mu\; L}{{wh}^{3}( {1 - {0.63\frac{h}{w}}} )}.}} & (6)\end{matrix}$

Assuming constant L and h, Equation (6) illustrates that the fluidicresistance of a waste channel can be controlled by changing its width.Thus, amount of fluid drawn through a secondary channel can becontrolled by the width of the secondary channel, which is given by theformula:

$\begin{matrix}{w \approx {\frac{12\mu\; L}{h^{3}R_{H}} + {0.63\mspace{11mu}{h.}}}} & (7)\end{matrix}$

The lengths for curvilinear channel sections of the spiral, L_(arc),were calculated using

${L_{arc} = \frac{\alpha\;\pi\; R}{180}},$where α is the angle in degrees and R is the radius of curvature.

Equation (7) is only valid for the case of w>h. However, when attemptingto remove only a small fraction of fluid, a thin channel may berequired, and thus the width may be less than the height. For this case,the full Equation (5) should be solved to determine the width, whichrequires a numerical solver.

To design the system for a targeted performance, the waste channel widthis set in order to remove a targeted fraction of the sample fluid. Thefraction of fluid removed through a waste channel, x_(s,j), is relatedto r_(Q,j) through

$\begin{matrix}{x_{s,j} = \frac{1}{1 + r_{Q,j}}} & (8)\end{matrix}$where the fraction of the flow remaining in the main channel, x_(m,j),is given by

$\begin{matrix}{x_{m,j} = {\frac{r_{Q,j}}{1 + r_{Q,j}}.}} & (9)\end{matrix}$

By simply specifying the ratio of volumetric flow between the mainchannel and a waste channel (r_(Q,j)), a spiral inertial filtrationdevice can be designed for the removal of a specific fraction of theinlet fluid.

Validation of Design Equations

The rate of fluid removal from the main channel via the secondary, orwaste, channel is controlled by designing for a specific flow ratio(r_(Q)=Q_(m)/Q_(s)) of main channel flow to secondary channel flow. Therelative volumetric flow rates through the main (Q_(m)) and secondarychannel (Q_(s)) are achieved by properly balancing the fluidicresistances in the channels. Thus, the fraction of fluid removed from aSIFT device can be controlled by designing for a specific flow ratio,r_(Q,j), at each waste channel, which is achieved by properly balancingthe fluidic resistances. To verify the design defined by the equationsderived above, devices designed for removal of 5, 10, 20, and 50% of theinlet fluid through a single waste channel were fabricated and tested.The waste channel was located at the W2 position (See FIG. 4). Aschematic of the waste channel is shown in FIG. 6A. As described above,the width of the waste channel, w_(s,j), was set to control the amountof fluid removed from the main channel. The main channel width prior tothe waste channel, w_(m,j), and the main channel width after the wastechannel, w_(m,j-1), were both 250 μm.

FIG. 6B shows the percentage of fluid removed through the waste channel(604) as a function of inlet volumetric flow rate for devices designedfor the removal of 5%, 10%, 20%, or 50% of the inlet fluid. The widthsof the main channel (602) w_(m) and the waste, or secondary, channels(604) w_(s) in μm are listed for each of the devices. The width of themain channel (602), w_(m,j), before the waste channel (604) is equal tothe width of the main channel (604) after the waste channel (604),w_(m,j-1) for each graph presented in FIG. 6B. The width of the wastechannel (604), w_(s)j, however, is shown as being different for eachgraph in response to the amount of fluid removed from the main channel(602). Specifically, the width of the main channel (602), w_(m,j),before the waste channel (604) and after the waste channel, w_(m,j-1),is 250 μm. Errors bars indicate the standard deviation across threeexperiments for a single device. To measure variation due tofabrication, two conditions were tested with duplicate devices: 20%fluid removal at 50 μL/min and 10% fluid removal at 1000 μL/min. The 20%results agreed to within 1.5%, and the 10% results were within 0.5%.

At low flow rates, the fraction of fluid removed was within 2% of thedesigned value. With increasing flow rate, the fraction decreased,flattening at 1000 μL/min, although the removal rates were still within6%. According to Equation(4), the fluid removal rate should beindependent of flow rate. The flow rate dependence was attributed to theelasticity of the PDMS. It is known that deformation of PDMSmicrochannels occurs under pressure-driven flow, causing changes in thechannel height and width^(73,74). The design equations did not accountfor this behavior. As a result, for the flow rates at which operationwas desired (>750 μL/min), the fluid removal rates were different thanwhat was designed. The widths of the waste channels could be adjusted toaccount for PDMS deformation, or other materials can be used that do notswell under pressure, such as thermal plastics.

Equation (7) was used to design these devices even though for the 5%removal width, w, of the waste channel is less than height, h, of thewaste channel so this approximation was not valid. For that 5% device,the difference in widths calculated by solving Equation (5) and Equation(7) is 5 μm. Given the fabrication tolerances (see above), a 5 μmdifference in the widths was deemed to be acceptable. FIG. 6B shows 5%fluid removal to within ±1.5%.

EXAMPLES Example 1 Device Fabrication

To evaluate the design methodology, a series of SIFT microfluidicdevices with a single waste channel (at the W2 position in FIG. 4) werefabricated. These devices consisted of a 7-loop Archimedean spiral(inner radius of 0.5 cm) with a single inlet, a waste channel, and abifurcating outlet. In this non-limiting example, the spiral channel was250 μm×50 μm (w×h) and had a 250 μm gap between successive loops. Theevaluation design chosen is not intended to be limiting. The inventionmay be implemented with main channel conigurations having fewer than ormore than seven loops or configurations other than an Archimedean spiralof the stated dimensions. The widths of the waste channels were setbetween 40 and 250 μm to remove a certain fraction of fluid: e.g., 5,10, 20, or 50%. As discussed below, the flow removed by a waste channeldepends on its fluidic resistance, which is proportional to the channellength divided by its width. The soft lithography technique that wasused achieved widths within 2-5 μm of the designed widths. Therefore, todistinguish devices designed to remove different amounts of fluid, thewaste channel widths needed to differ by more than 5 μm. Ensuring thistolerance necessitated a waste channel length of 19 mm, which was fitcompactly next to the spiral using a meander path (see FIG. 4).

Subsequently, to demonstrate a concentration increase of greater than anorder of magnitude for separated and recovered particles, a device witha series of 6 waste channels was fabricated. This device was similar tothe single waste channel devices except that it consisted of a 6-loopArchimedean spiral, six waste channels, and five branched outlets (FIG.4). In this non-limiting example, each of the waste channels was 35 μmwide, 50 μm high, and 19 mm in long.

The goal of the SIFT device containing six waste channels and fiveoutlets was to achieve fluid removal rates r_(Q) larger than an order ofmagnitude. For W3-W6 r_(Q) was 5, and for W1 and W2 r_(Q) was 10. Thefive outlets, each having an r_(Q) of 4, were used to further increasethe amount of fluid separated from the recovered particles. Table 1lists the r_(Q) and the calculated fraction of fluid removed from thewaste channels, x_(s,j,calc), wherein the subscript “s” refers tosecondary, or waste, channels.

The waste channel width, w_(s,j,calc), required to achieve these r_(Q)was calculated. To be able to use Equation (7), the w_(s,j,calc) must begreater than h (50 μm); if not, the error from using the approximationwas>10 μm. To achieve the desired fluid removal, w_(s,j,calc) would be<h(50 μm), and so the full Equation (5) was solved to calculatew_(s,j,calc) (see below for a discussion on using Equation (5) for w>hand w≈h). The w_(s,j,calc) are listed in Table 1. With the exception ofW2, they were within 4 μm of each other, and, as mentioned previously,fabrication tolerances were 2-5 μm. The waste channels were thereforeall (including W2) made 35 μm wide (w_(s,j,rev)), where “rev” indicatesrevised parameters. This value was conservative to ensure thatfabrication variations or expansion of the polydimethylsiloxane (“PDMS”)microchannels (discussed below) would still result in channels thatyielded the desired fluid removal. The width of the main channelfollowing channels W3 -W6, w_(m,j-1,calc), was adjusted (reduced) tomaintain U_(f) and compensate for fluid removed from the main channelthrough the waste channels (described in more detail below). Using a 35μm width for each of the waste channels and the w_(m,j-1,calc), thefraction of fluid to be removed from the waste channels, x_(s,j,rev),was determined (Table 1).

TABLE 1 List of parameters and dimensions for the multi-waste-channelspiral inertial filtration device shown in FIG. 4 (the standarddeviation of five trials is indicated by ±). W_(m,j−1,rev) W_(s,j,calc)W_(s,j,rev) Channel r_(Q) x_(s,j,calc) x_(s,j,rev) x_(s,j,exp) (μm) (μm)(μm) Inlet — — — — 250 — — W6 5 0.17 0.13 0.14 ± 0.010 210 41 35 W5 50.17 0.13 0.18 ± 0.016 175 40 35 W4 5 0.17 0.13 0.15 ± 0.006 145 40 35W3 5 0.17 0.13 0.16 ± 0.005 120 40 35 W2 10 0.09 0.11 0.15 ± 0.003 11032 35 W1 10 0.09 0.08 0.12 ± 0.003 100 37 35 O1 4 0.20 0.20 0.19 ± 0.010— 75 75 O2 4 0.20 0.20 0.21 ± 0.012 — 75 75 O3 4 0.20 0.20 0.19 ± 0.029— 75 75 O4 4 0.20 0.20 0.20 ± 0.006 — 75 75 O5 4 0.20 0.20 0.20 ± 0.008— 75 75

The fractions of fluid collected experimentally from each waste channeland outlet, x_(s,j,exp), are given in the 5^(th) column of Table 1. Theexperimental values, x_(s,j,exp), closely matched x_(s,j,rev), differingby less than 5% in all cases. For a particle stream collected out of asingle outlet, this would result in ˜93% removal of fluid and a particleconcentration factor of 13.

The devices were fabricated using standard soft lithography. A 10:1mixture of polydimethylsiloxane (PDMS) prepolymer and curing agent(Sylgard 184, Dow Corning) was cast over a silicon master mold and curedat 50° C. for two hours. The master mold was formed by spin coatingphotoresist (Shipley 1813) onto a silicon wafer to a thickness of 3 μm,pre-baking for 1 min at 95° C., and exposing to 365 nm UV for 13 s. Thephotoresist was developed for 75 sec. in Microposit developer CD-30(Shipley). The wafer was then etched at a rate of ˜2 μm/min with deepreactive ion etching (DRIE) using the photoresist as the mask. Theresist was stripped using Remover PG (MicroChem Corp.). To aid in therelease of the cured PDMS, the silicon mold was silanized withtrichloro(1H, 1H, 2H, 2H-perfluorooctyl)silane (Sigma Aldrich) usingvapor deposition. Inlets and outlets were punched into the PDMSsubstrate, and it was sonicated in isopropanol for 90 min to remove PDMSdebris and dust. The PDMS substrate was placed on an 85° C. hotplate for2 hrs to remove the isopropanol and was then irreversibly bonded toglass using O₂ plasma (13 seconds at 0.75 Torr and 50 mW). Tygon tubing(0.02″ I.D., 0.06″ O.D.) was inserted into the inlet and outlets of thebonded devices.

Example 2 Fluid Removal Quantification

To determine the amount of fluid removed by the waste channels,deionized water was pumped into the devices at particular flow ratesusing a syringe pump (New Era Pump Systems, Inc.). To ensure that theflow rate had stabilized, each rate was held for 5 minutes. Fluid wasthen collected from the waste channels and the outlets for 5 min and thefluid was weighed to determine the volume collected. This was repeatedthree times for each flow rate for a single device.

Example 3 Particle Focusing

FIG. 7 represents images of 15 μm particles focused in SIFT devicescontaining a single waste channel (704) designed for 5% (i and ii), 20%(iii and iv), and 50% (v and vi) fluid removal at two flow rates (100μL/min and 1250 μL/min). The flow rates selected for experiment andverification are not intended to be limiting. Flow rates different from100 μL/min or 1250 μL/min may be used and higher flow rates, e.g., up to3 mL/min. may be employed. FIG. 7 showed that one can design forspecific fluid removal rates; however, it is important to determine theimpact of the fluid removal on the concentration and position of focusedparticle streams (712). Fluorescent particles 15 μm in diameter (14%coefficient of variation (CV)) (ThermoFisher Scientific) dispersed indeionized water at a concentration of 0.003% by weight were injected atincreasing flow rates into the spiral inertial filtration devicescontaining a single waste channel (704) of varying width using thesyringe pump. Images of the focused particles were taken using aninverted fluorescence microscope (Olympus Corporation, model IX51)equipped with a 12-bit digital CCD camera (Hamamatsu Photonics, modelORCA-03G). Three-second exposures were used to create visible particletraces. A sequence of 15 images was overlaid to create a compositeimage. To visualize the channel walls, a bright field image was taken,the image was inverted (converted to a negative) using ImageJ (U.S.National Institutes of Health), and the image was overlaid onto theparticle focusing composite to create the final image.

At low fluid removal rates (5%), there was little effect on the focusedparticle stream (712) (FIGS. 7i and ii). With increasing flow rate, theparticle stream moved from an equilibrium position near the center (FIG.7i ) to a new equilibrium position closer to the inner wall (714) (FIG.7 ii). This behavior was expected and was recently illustrated by Marteland Toner⁵¹.

At a fluid removal rate of 20% (FIGS. 7 iii and iv), there was anoticeable change of ˜17 μm in the position of the focused particlestream (712) as it went past the waste channel (704). As fluid isremoved, the average velocity in the channel U_(f), along with De,decreases. For 100 μL/min (FIG. 7 iii), U_(f) decreased from 0.13 m/s to0.11 m/s and De decreased from 0.79 to 0.63 after removal of 20% of thefluid. This was accompanied by an increase in the width of the particlestream (712) and a shift in the particle stream position. Previousreports have shown that the width of particle streams (712) in a spiralchannel increases with decreases in U_(f) ⁵¹. The position shift islikely due to distortions in the fluid streamlines caused by the largefluid removal rates, drawing the particle stream toward the wastechannel. At the higher flow rate (FIG. 7 iv), the impact of the wastechannel (704) on the particle stream decreased because the particlesoccupied streamlines closer to the inner wall, which are less affectedby the waste channel (704) (FIG. 7 iv). In addition, as the streamlinesare distorted, the width of the streamlines increases, causing a furtherincrease in the width of the particle stream (710).

At 50% fluid removal (FIGS. 7v and vi), the shift in particle positionand increase in particle stream width were exacerbated. At a flow rateof 100 μL/min (FIG. 7v ), the distortion of the particle stream (˜100μm) caused some of the particles to be drawn out of the waste channel(704) (faint particles traces not easily visible in the figure). Even athigh flow rates (FIG. 7 vi), the particle stream (712) was affected bythe fluid removal. Following the waste channel (704), the particlestream partially recovered because of the focusing nature of the spiralgeometry; however, the large decrease in U_(f) and De from 0.13 m/s to0.07 m/s and 0.79 to 0.40, respectively, resulted in a wider particlestream that did not fully refocus. In practice, this limits the amountof fluid that can be removed from one waste channel without adverselyaffecting the results to ˜20%. At higher fluid removal rates losses inrecovery and separation efficiency will occur.

Channel Width Correction

To achieve high fluid removal rates without dispersing the particles asthey pass the waste channels, at least one of U_(f) and De must bemaintained by modifying conditions of the main channel flow downstreamof the waste channel. This can be most easily accomplished by changingthe width of the main channel following the waste channel. However,U_(f) and De have different dependences on the channel width and cannotbe simultaneously corrected. As a result, the effect of correcting eachindividually was investigated to determine which parameter had thelargest impact on focusing.

To maintain De, the width of the main channel following the j^(th) wastechannel, w_(m,j-1), was calculated using

$\begin{matrix}{{\frac{w_{m,{j - 1}} + h}{w_{m,{j - 1}}^{1/3}} = ( \frac{2x_{m,j}Q_{m,{j - 1}}\rho\; h^{1/2}}{\mu\; R^{1/2}{De}} )^{2/3}},} & (10)\end{matrix}$which was obtained by taking Equation (1) and substituting in Equation(2) and U_(f,m,j-1)=x_(m,j)Q_(m,j-1)(w·h)⁻¹.

Devices with a single waste channel and corrected main channel widthsfor three removal rates were fabricated to experimentally confirm theprediction of Equation (10) on maintaining De. The downstream corners ofthe waste channels were filleted to allow for a gradual change to thecorrected width of the main channel. Fluorescent particles of 15 μmdiameter at a concentration of 0.003% were injected into the threedevices. FIG. 8A represents particle focusing results for SIFT deviceswith the main channel widths corrected to maintain Dean number, De,following fluid removal from a single waste channel. FIG. 8A shows theparticle stream (812) at fluid removal rates of 5, 20, and 50% at 100μL/min and 1250 μL/min. As expected for a low fluid removal rate, at 5%there was no noticeable impact on the position or width of the particlestream (812) due to the presence of the waste channel (804) (See FIGS.8Ai and ii). For low fluid removal rates, it is unnecessary to correctw_(m,j-1) because De does not change significantly enough to impactparticle focusing.

At 20% removal, the influence of the waste channel was effectivelyminimized by the width correction (compare FIGS. 8A iii and iv withFIGS. 7 iii and iv). For a flow rate of 1250 μL/min, the waste channel(804) had no impact on the particle stream (812) (See FIG. 8A iv). At100 μL/min, the particles maintained an almost fixed position relativeto the inner wall (See FIG. 8A iii), unlike the case without Decorrection, in which the particles shifted towards the waste channel(See FIG. 7 iii). In fact, there was a minute shift (13 μm) of theparticle stream (812) in FIG. 8A iii toward the inner wall (814) as aresult of the change in w_(m,j-1). This occurs because changingw_(m,j-1) to correct for De results in a different channel aspect ratio(w/h) following the waste channel (804). It has been shown that particlestream width and position depend on the aspect ratio; at a smalleraspect ratio particles occupy an equilibrium position closer to theinner wall.⁵¹

For 50% fluid removal, there was a sizeable distortion in the particlestream (812) at 100 μL/min (See FIG. 8A v). However, unlike for theuncorrected devices, particles did not exit the waste channel (804), andfollowing the waste channel (804), the particle stream (812) refocusedto a new equilibrium position. Again, the change in position of thefocused stream can be explained by the change in aspect ratio: tocorrect for 50% fluid removal, w_(m,j-1) was decreased from 250 μm to 80μm, a change in the aspect ratio from 5 to 1.6. The normalized particleposition, defined as the distance from the inner wall (814) over thetotal channel width, prior to the waste channel was 0.42, and after thewaste channel it was 0.7. Unlike for the 20% fluid removal case (FIG. 8Aiii), the resulting shift in focusing position was towards the outerhalf of the channel. This behavior was unexpected, and the underlyingphysics is not yet known, but it was suspected that the initial particleposition before the sudden large change in channel width plays a role.Such shifts could limit the amount of fluid removed using this strategyat the low flow rate of 100 μL/min. If a second waste channel removing asizeable fraction of fluid were located further downstream, it is likelythat the particle stream would be drawn out of the second waste channel(804). For 100 μL/min, this limits the fluid removal to ˜50%, far shortof the >90% desired. However, for 1250 μL/min the particle stream fullyrecovered after the waste channel. Again, the change in the aspect ratiohad a noticeable effect on the particle stream, which, as expected,moved closer to the inner wall (814). At this speed, further removingfluid through downstream waste channels (804) is possible, allowing bothhigher fluid removal and greater particle concentration factors to beachieved simultaneously, a significant benefit of this designs.

One of the major limitations of adjusting channel width to maintain Deis that as fluid is removed from sequential waste channels (FIG. 4) andw_(m,j-1) is adjusted after each one, eventually the channel becomes toonarrow to continue. Martel and Toner⁵¹ showed that as the aspect ratio(w/h) approaches unity, particle confinement, defined as the ratio ofthe channel width to the particle stream width, decreases. If theparticle streams occupy a larger fraction of the channel, particles ofdifferent sizes come into close proximity or even overlap, makingseparation difficult.

The approach of correcting the width to maintain the fluid velocity,U_(f), was tested to determine if this provides an advantage as comparedto correction for De. In this case, the new width depends only on thefraction of fluid remaining in the main channel, x_(m,j-1), and thewidth of the previous section of main channel, w_(m,j):w_(m,j-1)=x_(m,j-1)w_(m,j).

FIG. 8B shows the results of focusing 15 μm fluorescent particles indevices designed to maintain fluid velocity, U_(f), following fluidremoval from a single waste channel. The waste channel had little to noeffect on the particle stream for 5% removal (See FIGS. 8Bi and ii) and20% removal (See FIGS. 8B iii and iv). The results were similar to thoseobtained for maintaining De (compare FIGS. 8A i, ii, iii, iv) becausew_(m,j-1) corrected for De and U_(f) for 5% removal and 20% removaldiffered by only 4% and 7%, respectively. For 50% fluid removal, thew_(m,j-1) was 36% larger for the U_(f) correction than for the Decorrection. At the 100 μL/min flow rate, the particle stream recoveredin both cases but to different equilibrium positions (compare FIGS. 8A vand 7 v), and at 1250 μL/min the two results were nearlyindistinguishable, even though the De in FIG. 8A vi is 9.87 followingthe waste channel and in FIG. 8B vi it is 7.83.

FIG. 8 shows that correcting for either De or U_(f) eliminated particleloss through the waste channel (804) and improved focusing after thewaste channel (804). However, there are advantages to the U_(f)correction. For low flow rates (100 μL/min), U_(f) correction preventedparticle stream dispersion at the waste channel (FIG. 8B). The particlestream (812) maintained its trajectory at a normalized particle positionof 0.45. In addition, since the corrected width for U_(f) is wider thanfor De, more fluid can be removed from sequential waste channels withoutnegatively affecting particle focusing and separation.

In an alternate embodiment, the main channel (802) of the device mayhave a non-uniform height varying along the length of the main channel(802) so that the channel geometry could be varied to maintain asubstantially constant De or U_(f) by varying the height instead of, orin addition to, varying the width. In one such alternate embodimenthaving more than one secondary channel, the height of the main channelis substantially constant between each two neighboring secondarychannels.

Other corrections that could be made to sustain particle focusing afterfluid removal, other than, or in addition, to De and U_(f), by modifyingthe geometry of the main channel 1250 (e.g., height and/or width) arefor Reynolds number and particle Reynolds number.

To evaluate particle separation from a fluid stream containing particlesof more than one particle size, 4.8 μm (5% CV) (Duke Scientific Corp.)and 8 μm (18% CV) (ThermoFisher Scientific) fluorescent particlesdispersed in deionized water at a concentration of 0.001% by weight wereinjected into the multi-waste-channel SIFT device (FIG. 4) at a flowrate of 950 μL/min. The flow was allowed to equilibrate for 5 minutes.Fluid was collected from the waste channels (804) and the outlets intovials for 5 minutes. Particles in each vial were counted using ahemocytometer (INCYTO). The separation was repeated five times with twodevices (n=3 in one device and n=2 in the second device).

These results are shown in FIGS. 9A-9C. FIG. 9A represents fluorescentimages showing the separation of two particle sizes, 4.8 μm and 8 μm, ina SIFT device designed for removal of 93% of the inlet fluid. The twoparticle sizes were completely separated at W6 (FIG. 9A i). Because ofthe main channel width correction (main channel width after the wastechannel is smaller than before the waste channel), the particle streams(912) and (914) were not impacted by the waste channels (904). Even atW1, where 63% of the inlet fluid was removed, there was no noticeableimpact on the particle streams (912) and (914) (FIG. 9A ii). Due to thechange in the aspect ratio and the decreased particle confinement, theseparation between the two particle streams (912) and (914) decreased,but the two sizes were still clearly separated. The channel (902) wasexpanded (FIG. 9A iii) to allow for the two particle streams to beseparated into different outlets, with the 8 μm (red) particles flowingout of O1 (916) and the 4.8 μm particles out of O2 (918) (FIG. 9A iv).

FIG. 9B is a graph of separation efficiency, calculated as the number ofparticles collected at each outlet over the number input into thedevice. Error bars are standard deviations from 5 experiments in twodevices (n=3 in one device and n=2 in the other). A separationefficiency of 100.4±6.2 and 95.2±9.9 was achieved for the 4.8 μm and 8μm particles, respectively. (The separation efficiency greater than 100%is attributed to errors associated with particle counting using ahemocytometer.) FIG. 9C is a graph of particle concentration factor(concentration at each outlet, assuming 100% recovery, over the inletconcentration multiplied by the separation efficiency). Again, errorbars are standard deviations from 5 experiments in two devices (n=3 inone device and n=2 in the other). Since each particle stream wasseparated into a different outlet, the total fluid removed for eachparticle size was ˜93%, which corresponded to a concentration factor of13.4±0.82 for the 4.8 μm particles and 12.7±0.99 for the 8 μm particles(FIG. 9C).

Streams (1212) and (1214) of two particle sizes, 4.8 μm and 8 μm, in aspiral inertial filtration (SIFT) device containing 6 waste channels(1204) and five outlets (1216)-(1224) are shown in FIG. 12 at each wastechannel (1204) W1-W6 and at the outlets (1216)-(1224), 1-5. The particlestreams are clearly separated at every location.

Derivation of Waste Channel Resistance Equation (4)

To simplify the derivation, an illustration is provided using a devicewith three waste channels. The equivalent circuit is shown in FIG. 10.Note that the numbering is from back to front, so “first” means “firstfrom the end”. The constant flow rate produced by the syringe pump ismodeled as a current source.

The derivation begins with the resistance of the first (right-most inFIG. 9A) leg of the main channel R_(m,1) and the resistance of the firstside waste channel, R_(s,1). Using an equivalent circuit analogy, inwhich the pressure drop ΔP is like a voltage and the fluid flow Q islike current, it is possible to write expressions analogous to Ohm's law(V=IR) for pressure-driven flow, known as Hagen-Poiseuille's law(ΔP=QR):ΔP_(s,1)=Q_(s,1)R_(s,1)   (13)ΔP_(m,1)=Q_(m,1)R_(m,1)   (14)where ΔP_(s,1) and ΔP_(m,1) are the pressure drops in the waste channeland the main channel, respectively, and Q_(s,1) and Q_(m,1) are thecorresponding volumetric flow rates, respectively. (See Oh et al.⁷⁵ foran excellent review of fluidic equivalent circuits with numerousexamples). ΔP_(s,1)=ΔP_(m,1) because they both start at the same point,and thus have the same pressure on their left sides, and both end at thesame point, which is atmospheric pressure (or ground) on their rightsides. Defining r_(Q,1) as the volumetric flow ratio between this mainand secondary channel,r _(Q,1) =Q _(m,1) /Q _(s,1),   (15)Equations (13), (14), and (15) are combined to yield the hydraulicresistance of the first waste channel, R_(s,1):R_(s,1)=r_(Q,1)R_(m,1).   (16)

Similarly, ΔP_(s,2) for the second waste channel, which also connects toground, isΔP_(s,2)=Q_(s,2)R_(s,2).   (17)

However, to determine the resistance of the second main channel,R_(m,2), a different approach is needed. The pressure drop ΔP_(m,2) isnot known (it does not terminate at atmospheric pressure), and soR_(m,2) cannot be obtained directly. To find it, an equivalentresistance, R_(EQ,2), across the combination of the second main channelsegment and the first two channels is defined, incorporating R_(m,2),R_(m,1), and R_(s,1):

$\begin{matrix}{R_{{EQ},2} = {R_{m,2} + \frac{1}{\frac{1}{R_{s,1}} + \frac{1}{R_{m,1}}}}} & (18)\end{matrix}$where R_(m,1) and R_(s,1) are in parallel and R_(m,2) is in series (FIG.11).

Inserting Equation (16) into Equation (18) and rearranging yields

$\begin{matrix}{R_{{EQ},2} = {R_{m,2} + {\frac{R_{s,1}}{1 + r_{Q,1}}.}}} & (19)\end{matrix}$

The pressure drop across R_(EQ,2) isΔP_(EQm,2)=Q_(m,2)R_(EQ,2)   (20)where Q_(m,2) is the volumetric flow rate of the second main channel,and since ΔP_(EQm,2) and ΔP_(s,2) start at the same node and bothterminate at ground, thenΔP_(EQm,2)=ΔP_(s,2).   (21)

Combining Equation (17), (19), (20), and (21) and defining a volumetricflow ratio of r_(Q,2)=Q_(m,2)/Q_(s,2) gives

$\begin{matrix}{R_{s,2} = {{r_{Q,2}\lbrack {R_{m,2} + \frac{R_{s,1}}{1 + r_{Q,1}}} \rbrack}.}} & (22)\end{matrix}$

The resistance of the third side waste channel, R_(s,3), is found in thesame manner. The pressure drop across R_(s,3) isΔP_(s,3)=Q_(s,3)R_(s,3).   (23)

Again, the pressure drop across the third main channel, ΔP_(m,3), isunknown and so an equivalent pressure, ΔP_(EQm,3), is defined asΔP_(EQm,3)=Q_(m,3)R_(EQ,3)   (24)where R_(EQ,3) is the equivalent resistance and is given by

$\begin{matrix}{R_{{EQ},3} = {{R_{m,3} + \frac{1}{\frac{1}{R_{s,2}} + \frac{1}{R_{{EQ},2}}}} = {R_{m,3} + \frac{1}{\frac{1}{R_{s,2}} + {\frac{1}{R_{m,2} + \frac{R_{s,1}}{1 + r_{Q,1}}}.}}}}} & (25)\end{matrix}$

From Equation (22) it can be seen that

$\begin{matrix}{{\frac{R_{s,2}}{r_{Q,2}} = {R_{m,2} + \frac{R_{s,1}}{1 + r_{Q,1}}}},} & (26)\end{matrix}$so Equation (24) can be rewritten as

$\begin{matrix}{R_{{EQ},3} = {R_{m,3} + {\frac{R_{s,2}}{1 + r_{Q,2}}.}}} & (27)\end{matrix}$

Again ΔP_(s,3)=ΔP_(EQm,3). Combining Equations (23), (24), and (27) anddefining r_(Q,3)=Q_(m,3)/Q_(s,3) gives

$\begin{matrix}{R_{s,3} = {{r_{Q,3}\lbrack {R_{m,3} + \frac{R_{s,2}}{1 + r_{Q,2}}} \rbrack}.}} & (28)\end{matrix}$

Equations (22) and (28) can be written in the general form

$\begin{matrix}{R_{s,j} = {r_{Q,j}\lbrack {R_{m,j} + \frac{R_{s,{j - 1}}}{1 + r_{Q,{j - 1}}}} \rbrack}} & (29)\end{matrix}$shown in Equation (4) for j=2, 3, 4, . . . , n−1, n.

Hydraulic Resistance.

For Equation (5) to be valid, the width of the channel, w, must begreater than the height, h. As previously discussed, for some casesEquation (5) can be simplified to Equation (7). Whether Equation (7) isvalid will depend on the specific parameters of the system.

For w<h, a variation of Equation (5) can be used. The hydraulicresistance of a rectangular channel depends on its cross-sectional area,so the resistance of a rectangular channel with dimensions w×h is thesame as that of a channel with “w” and “h” reversed. In other words,rotating a rectangular channel by 90° does not change its resistance. Todetermine the hydraulic resistance of a channel with w<h, one cantherefore rewrite Equation (5) with w and h reversed, as

$\begin{matrix}{R_{H} = {\frac{12\mu\; L}{{hw}^{3}}{( {1 - {\frac{192w}{\pi^{5}h}{\sum\limits_{{n = 1},3,5,\;\ldots}^{\propto}\frac{\tanh\mspace{11mu}( \frac{n\;\pi\; h}{2w} )}{n^{5}}}}} )^{- 1}.}}} & (30)\end{matrix}$

A study for h=50 μm, L=19 mm, n=1, and μ=10⁻³ Pa s⁻¹ was performed todetermine the thresholds at which Equation (5), Equation (7), andEquation (30) could be used for widths w ranging from 10 μm to 200 μm(i.e. aspect ratios ranging from 0.2 to 4). The results are shown inTable 2.

TABLE 2 Hydraulic resistance calculated using three different equationsfor various w and with h = 50 μm. Results within 10% are highlighted.Difference from Aspect Hydraulic Resistance, R_(H) Eq. (5) (%) Width,Ratio (Pa m³ s⁻¹) Eq. (7) Eq. (30) w (μm) (w/h) Eq. (5) Eq. (7) Eq. (29)approximation w 

 h 10 0.2 3.99 × 10¹⁵ NA* 5.21 × 10¹⁵ — 30.52 25 0.5 4.12 × 10¹⁴ NA*4.25 × 10¹⁴ — 3.04 30 0.6 2.64 × 10¹⁴ NA* 2.69 × 10¹⁴ — 1.81 35 0.7 1.84× 10¹⁴ 5.21 × 10¹⁴ 1.86 × 10¹⁴ 182.65 1.10 40 0.8 1.37 × 10¹⁴ 2.15 ×10¹⁴ 1.38 × 10¹⁴ 56.83 0.63 45 0.9 1.06 × 10¹⁴ 1.35 × 10¹⁴ 1.07 × 10¹⁴26.92 0.29 50 1.0 8.59 × 10¹³ 9.86 × 10¹³ 8.59 × 10¹³ 14.75 0.00 55 1.17.14 × 10¹³ 7.76 × 10¹³ 7.12 × 10¹³ 8.72 0.26 60 1.2 6.07 × 10¹³ 6.40 ×10¹³ 6.04 × 10¹³ 5.42 0.50 65 1.3 5.26 × 10¹³ 5.44 × 10¹³ 5.22 × 10¹³3.49 0.75 70 1.4 4.63 × 10¹³ 4.74 × 10¹³ 4.58 × 10¹³ 2.32 1.01 75 1.54.13 × 10¹³ 4.19 × 10¹³ 4.07 × 10¹³ 1.58 1.28 80 1.6 3.72 × 10¹³ 3.76 ×10¹³ 3.66 × 10¹³ 1.11 1.57 85 1.7 3.38 × 10¹³ 3.41 × 10¹³ 3.32 × 10¹³0.80 1.88 90 1.8 3.10 × 10¹³ 3.12 × 10¹³ 3.03 × 10¹³ 0.60 2.22 95 1.92.86 × 10¹³ 2.87 × 10¹³ 2.79 × 10¹³ 0.46 2.57 100 2.0 2.65 × 10¹³ 2.66 ×10¹³ 2.57 × 10¹³ 0.36 2.95 200 4.0  1.08 × 10⁻¹³  1.08 × 10⁻¹³ 9.17 ×10¹² 0.08 15.26 NA indicates that the calculated resistance wasnegative.

For the parameters used here, Equation (7) was a good approximation forall aspect ratios w/h>1 (w>50 μm): the percent difference was less than10%. Above w/h=1.6, the percent difference was less than 1%. Asexpected, using the simplified Equation (7) for w/h≤1 introduced error,with the magnitude of the error increasing strongly as w/h decreased.

Interestingly, the error associated with using Equation (5) instead ofEquation (29) was small even for w<h until w/h<0.5. For w/h=2 to 0.5,Equations (5) and (29) differed by less than 3%, so they could be usedinterchangeably. In other words, for w≈h both Equation (5) and Equation(29) were valid. Beyond these aspect ratios, the correct equation,either Equation (5) or Equation (29) must be used.

Techniques that can quickly process large sample volumes while achievingefficient recovery and enrichment of rare particles are necessary forlab-on-a-chip (LOC) applications that require a large volume reductionin order to enable subsequent microfluidic processing steps. In thiswork, a spiral inertial filtration (SIFT) device capable of achievingparticle concentration factors of 13× (removal of 93% of the inletfluid) at ˜1 mL/min was presented. The amount of fluid removed wasaccurately controlled by designing a device with the fluidic resistancesprecisely balanced between the main flow channel and the waste channels.By ensuring that the fluid velocity in the main channel was maintainedfollowing each fluid removal, removal of large fractions of the inletfluid was possible without disrupting the focused particle streams,yielding nearly 100% separation efficiency.

It will be appreciated that the methods and compositions of the instantinvention can be incorporated in the form of a variety of embodiments,only a few of which are disclosed herein. Embodiments of this inventionare described herein, including the best mode known to the inventors forcarrying out the invention. Variations of those embodiments may becomeapparent to those of ordinary skill in the art upon reading theforegoing description. The inventors expect skilled artisans to employsuch variations as appropriate, and the inventors intend for theinvention to be practiced otherwise than as specifically describedherein. Accordingly, this invention includes all modifications andequivalents of the subject matter recited in the claims appended heretoas permitted by applicable law. Moreover, any combination of theabove-described elements in all possible variations thereof isencompassed by the invention unless otherwise indicated herein orotherwise clearly contradicted by context.

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The invention claimed is:
 1. A method of filtering and/or concentratingparticles of a fluid containing particles of one or more particle sizes,said method comprising: moving the fluid in a spiral path from a fluidinlet along a length of a main fluid channel to one or more fluidoutlets, wherein the main channel has a non-uniform geometry, whereinthe geometry of the main channel is changed following one or moresecondary channels to compensate for fluid removal via the one or moresecondary channels causing differential migration of particles withinthe moving fluid into unique equilibrium positions according to the sizeof the particles thereby forming one or more particle streams and aparticle-free region within the moving fluid; drawing at least a portionof the fluid from the particle-free region of the moving fluid via theone or more secondary channels to increase the concentration ofparticles within the remainder of the moving fluid; and collectingparticles from one or more of the particle streams.
 2. The method ofclaim 1, wherein the collecting step is performed at an end of thespiral path.
 3. The method of claim 1, wherein the particles compriseone or more components of interest within a sample fluid.
 4. The methodof claim 3, wherein the drawing step increases concentration of eachcomponent of interest.
 5. The method of claim 1, wherein the particlesof each of the one or more particle streams are maintained inequilibrium positions by lift forces F_(L) and Dean forces F_(D).
 6. Themethod of claim 1, wherein the one or more particles sizes are in arange of 4.8 μm to 15 μm.
 7. The method of claim 1, wherein the drawingstep reduces the volume of the moving fluid by about 10-95%.
 8. Themethod of claim 1, wherein the particles are selected from the groupconsisting of DNA molecules, viruses, bacteria, fungi, cancer cells,white blood cells, and neutrophils.
 9. The method of claim 1, furthercomprising changing conditions of the moving fluid after the drawing atleast a portion of the fluid from the particle-free region of the movingfluid to maintain a constant or substantially constant flow velocitywithin the moving fluid before and after the drawing at least a portionof the fluid from the particle-free region of the moving fluid.
 10. Thefluid processing apparatus of claim 1, further comprising changingconditions of the moving fluid after the drawing at least a portion ofthe fluid from the particle-free region of the moving fluid to maintaina constant or substantially constant Dean number before and after thedrawing at least a portion of the fluid from the particle-free region ofthe moving fluid.
 11. The method of claim 1, wherein the moving fluidhas a flow rate of between 100 μL/min and 1250 μL/min.
 12. The method ofclaim 1, comprising filtering and/or concentrating fluid containingparticles of one or more particle sizes at a rate of 1 mL/min.
 13. Themethod of claim 1, wherein the step of drawing at least a portion of thefluid from the particle-free region of the moving fluid is performed inthe one or more secondary channels extending from the main fluidchannel; and the step of collecting particles from one or more of theparticle streams is performed with one or more outlets in fluidcommunication with said main fluid channel.
 14. The method of claim 13,wherein said one or more secondary channels extend radially outwardlyfrom an outer loop of the spiral configuration of said main channel. 15.The method of claim 13, wherein the collecting particles from eachparticle stream comprises collecting particles at between one and fivefluid outlets.
 16. The method of claim 13, wherein the drawing at leasta portion of the fluid from the particle-free region of the moving fluidwith comprises drawing of a portion of fluid with between one and six ofthe secondary channels.
 17. The method of claim 13, wherein eachsecondary channel extends from an outer edge of an outer-most ring ofthe spiral configuration of said main channel.
 18. The method of claim13, comprising wherein the drawing comprises drawing from 5 to 50% ofthe moving fluid in the main channel with each of said one or moresecondary channels.
 19. The method of claim 13, further comprisingdefining the width of each secondary channel to draw a specified portionof the fluid of the particle-free region from said main channelaccording to the formula:${w \approx {\frac{12\mu\; L}{h^{3}R_{H}} + {0.63\mspace{11mu} h}}},$wherein w is the width of the secondary channel, h is the height of thesecondary channel, L is the length of the secondary channel, μ is thedynamic viscosity of the fluid, and R_(H) is the hydraulic resistance ofthe secondary channel.
 20. The method of claim 13, wherein the spiralconfiguration of said main channel comprises a 7-loop spiral having aninner radius of about 0.5 cm, and said main channel comprises a width ofabout 250 μm and a height of about 50 μm.
 21. The method of claim 20,wherein said spiral main channel has a 250 μm gap between successiveloops.
 22. The method of claim 21, wherein the width of each secondarychannel is between 40 and 250 μm.
 23. The method of claim 22, whereinthe length of each secondary channel is about 19 mm.
 24. The method ofclaim 13, wherein each secondary channel comprises a width of about 35μm, a height of about 50 μm, and a length of about 19 mm.
 25. The methodof claim 1, wherein the main fluid channel has a non-uniform widthvarying along the length of the main channel.
 26. The method of claim25, wherein the one or more secondary channels comprise at least twosecondary channels and the step of drawing at least a portion of thefluid from the particle-free region of the moving fluid is performed bythe at least two secondary channels, and wherein a width of the mainchannel is substantially constant between each two neighboring secondarychannels.
 27. The method of claim 1, wherein the changing the geometryof said main channel following the at least one secondary channelmaintains a constant or substantially constant flow velocity within saidmain channel before and after the secondary channel.
 28. The method ofclaim 27, wherein the changing the geometry of said main channelcomprises changing a width of the main channel, wherein a new widthW_(m,j) of the main channel following a j^(th) secondary channel isdetermined by the formula:w_(m,j-1)=x_(m,j-1)w_(m,j), wherein x_(m,j-1)is the fraction of fluidremaining in the main channel after fluid removal through the j^(th)secondary channel, and w_(m,j) is a width of the previous section ofsaid main channel.
 29. The method of claim 1, wherein the changing thegeometry of said main channel following the at least one secondarychannel maintains a constant or substantially constant Dean number,D_(e), within said main channel before and after the secondary channel,wherein the Dean number, D_(e), is given by the formula:${De} = {\frac{\rho\; U_{f}D_{h}}{\mu}\sqrt{\frac{D_{h}}{2R}}}$ whereinρ is the density of the fluid, U_(f) is average fluid velocity, μ isfluid dynamic viscosity, R is a radius of curvature of said mainchannel, and D_(h) is a hydraulic diameter, and wherein the hydraulicdiameter, D_(h), is determined from: $D_{h} = \frac{2{wh}}{{w + h},}$wherein w is a width of said main channel and h is a height of said mainchannel.
 30. The method of claim 1, wherein the fluid resistance of asecondary channel of the one or more secondary channels required to drawfluid from the main channel at a specified rate satisfies therelationship:$R_{s,j} = {r_{Q,j}( {R_{m,j} + \frac{R_{s,{j - 1}}}{1 + r_{Q,{j - 1}}}} )}$where R_(s,j) is a fluid resistance of a j^(th) secondary channel at aj^(th) node where the j^(th) secondary channel connects to said mainchannel, R_(m,j) is a fluid resistance of said main channel at thej^(th) node, R_(s,j-1) is a fluid resistance of the secondary channel ata previous node j-1, and r_(Q,j-1) is a volumetric flow ratio of flowwithin said main channel (Q_(m,j)) to flow within the secondary channel(Q_(s,j)) at the j^(th) node.
 31. The method of claim 1, wherein thechanging the geometry of said main channel comprises changing a width ofthe main channel.
 32. A method of separating one or more particles froma sample fluid, comprising: moving the sample fluid in a spiral pathfrom a fluid inlet along a length of a main fluid channel to one or morefluid outlets, wherein the main channel has a non-uniform geometry,wherein the geometry of the main channel is changed following one ormore secondary channels extending from the main channel to compensatefor fluid removal via the one or more secondary channels causing theparticles within the moving sample fluid to be focused into one or moreparticle streams according to component size, thereby forming aparticle-free region within the moving sample fluid; drawing at least aportion of the sample fluid from the particle-free region of the movingsample fluid via the one or more secondary channels to increase theconcentration of particles within the remainder of the moving samplefluid; and collecting the particles from one or more of the particlestreams.